Finite element approximations of harmonic differentials on a Riemann surface (Q1822891)

This is a long and extensive paper introducing a method of applying finite element approximations on a Riemann surface. The method matches the abstract definition of Riemann surfaces and also can be applied to the case of plane domains. In section 1 the basic triangularization of the parametric disks is considered, the co-ordinates being local to the disks. In section 2 two spaces of differentials are introduced. In section 3 an harmonic differential on the Riemann surface, w, is approximated from the two spaces defined in 2. Finally two examples are given in section 4. Error estimates and extensive references are given.